Aabstract: In this talk we will discuss the Nehari type theorem, i.e., the characterization of the BMO space via the commutator of Riesz transforms, associated with operators in several different settings, where the analyticity or Fourier transform is not available. This is motivated by concrete examples arisen from harmonic analysis and differential equations, including the Cauchy integrals, the Reisz transforms associated with Neumann Laplacian, Bessel operators, and the sub-Laplacian on stratified nilpotent Lie groups (e.g. Heisenberg groups).